3.1: OneStep Equations
Learning Objectives
At the end of this lesson, students will be able to:
 Solve an equation using addition.
 Solve an equation using subtraction.
 Solve an equation using multiplication.
 Solve an equation using division.
Vocabulary
Terms introduced in this lesson:
 equal
 equation
 isolate
 linear equation
Teaching Strategies and Tips
Use the introductory problem to motivate equivalent equations, since it can be solved two ways:
 The cost plus the change received is equal to the amount paid, \begin{align*}x + 22 = 100\end{align*}
x+22=100 .  The cost is equal to the difference between the amount paid and the change, \begin{align*}x = 100  22\end{align*}
x=100−22
Examples 1 and 2 are essentially the same; constant terms must be added to both sides to isolate \begin{align*}x\end{align*}
Additional Example.
Solve \begin{align*}12 = 4 + x\end{align*}
Solution. To isolate \begin{align*}x\end{align*}
\begin{align*}12 & = \cancel{4} + x\\
+4 & = +\cancel{4}\\
16 & = x\end{align*}
The variable in Example 3 is not the usual \begin{align*}x\end{align*}
Solve \begin{align*}21=n+14\end{align*}
Hint: To isolate \begin{align*}n\end{align*}
In Examples 46, teachers may opt to solve the equations by adding the opposite in lieu of subtracting.
Example.
Solve \begin{align*}17=x+8\end{align*}
Hint: To isolate \begin{align*}x\end{align*}
\begin{align*}17 & = x+\cancel{8}\\
8 & = \cancel{8}\\
25 & = x\end{align*}
Use Example 6 as an example of an equation with fractions. Remind students to find common denominators.
Point out in Example 8 that in general,
\begin{align*}\frac{ax}{b}=\frac{a}{b}x\end{align*}
which will help students isolate \begin{align*}x\end{align*}
Note that the equation in Example 10 can be written in dollars or in cents:

\begin{align*}5x=3.25\end{align*}
5x=3.25 (\begin{align*}x\end{align*}x in dollars) 
\begin{align*}5x=325\end{align*}
5x=325 (\begin{align*}x\end{align*}x in cents)
Although Examples 13 and 15 can be solved by making a table and Example 14 by guessing and checking, teachers are encouraged to help students setup and solve an equation of the type presented in the lesson.
Error Troubleshooting
General Tip: After the constant term is canceled in a onestep equation, the variable must be carried down onto the next line. Remind students to write the \begin{align*}x =\end{align*}
General Tip: Students forget to perform the same operation on both sides of an equation. Have students use a colored pencil to write what they are doing to both sides of the equation.
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